Guiding metaheuristic to search for best of worst

ABSTRACT

Figures of merit by actual design parameters are tracked over iterations for candidate solutions that include both actual design parameters and actual context parameters. Instead of returning a current iteration figure of merit, a worst observed figure of merit for a set of actual design parameters is returned as the figure of merit for a candidate solution. Since the candidate solution includes both actual design parameters and actual context parameters and the worst observed figures of merit are tracked by actual design parameters, the figure of merit for a set of design parameters wilt be the worst of the observed worst case scenarios as defined by the actual context parameters over a run of a metaheuristic optimizer.

BACKGROUND

Embodiments of the inventive subject matter generally relate to thefield of computing, and, more particularly, to meta-heuristicoptimization.

Software tools employ metaheuristic optimization algorithms to solveoptimization problems. Metaheuristic optimization algorithms can becategorized as population-based and trajectory-based. Examples ofpopulation-based metaheuristic optimization algorithms includeevolutionary algorithms (e.g., genetic algorithm, differentialevolution), particle swarm optimization algorithms, ant colonyoptimization algorithms, and bee algorithms.

Metaheuristic optimization algorithms can be used to search a solutionspace for the best performing worst-case solution. That is, a designermay wish to optimize a design for situations where it is only theworst-case behavior that matters, For example, a designer might optimizean embedded circuit design to maximize performance under worst-caseprocess variations and operating environment. As another example, adesigner might optimize a system to minimize the worst-case powerconsumption.

Design problems have many variables. Some variables are under thecontrol of the designer, such as wire length and or thickness, Othervariables are outside the designer's control, such as manufacturingtolerances or environment variables (e.g., ambient temperature,humidity, data patterns, etc.). The worst-case environment for onedesign may not be the worst-case for another, Since the same set ofenvironmental/manufacturing variables can have different impacts upondifferent designs, designers search for the worst-case scenario for eachdesign under consideration, Also, the combined set of environment andmanufacturing variables can lead to a design space that is quite large,and difficult or impossible to exhaustively explore.

SUMMARY

Embodiments of the inventive subject matter relate to guiding apopulation-based metaheuristic to search for a best of worst cases foran optimization problem. For each candidate solution in a currentiteration of a population-based metaheuristic instance, it is determinedwhether a figure of merit generated from a fitness function of thepopulation-based metaheuristic instance for the candidate solution isworse than a figure of merit associated with actual design parameters ofthe candidate solution in a structure used to track worst observedfigures of merit by actual design parameters over iterations. The actualdesign parameters are a subset of actual parameters of the candidatesolution. The structure is updated to associate the figure of merit withthe actual design parameters when the figure of merit generated for thecandidate solution in the current. iteration is worse than a previouslyobserved worst figure of merit for the actual design parameters in thestructure. The worst between the figure of merit generated for thecandidate solution in the current iteration and the previously observedworst figure of merit for the actual design parameters is supplied as afigure of merit to be used for the candidate solution in advancing thepopulation-based metaheuristic instance.

BRIEF DESCRIPTION OF THE DRAWINGS

The present embodiments may be better understood, and numerous objects,features, and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 depicts an example conceptual diagram of a population-basedmetaheuristic optimizer persisting worst observed figures of merit byactual design parameters.

FIG. 2 depicts a flowchart of example operations for persisting theworst observed figure of merit across progression of a population-basedmetaheuristic optimizer.

FIG. 3 depicts a flowchart of example operations that avoid evaluationof candidate solutions with actual design parameters with previouslyobserved worst figures of merit already below a threshold (hereinafter“conservation threshold”).

FIG. 4 depicts a flowchart of example operations to enforce consistencyof worst observed figure of merit across observed same sets of actualdesign parameters within an iteration.

FIG. 5 depicts an example flowchart of operations for updating theprevious observed worst figure of merit.

FIG. 6 depicts an example network of nodes carrying out a multi-dememodel of a population-based metaheuristic optimization algorithm thatuses worst case evaluators.

FIG. 7 depicts an example computer system with a metaheuristic solverthat employs worst case evaluation.

DESCRIPTION OF EMBODIMENT(S)

The description that follows includes exemplary systems, methods,techniques, instruction sequences and computer program products thatembody techniques of the present inventive subject matter. However, itis understood that the described embodiments may be practiced withoutthese specific details. For instance, although examples refer to fitnessfunctions, embodiments may employ another objective function thatprovides values for comparing candidate solutions. In other instances,well-known instruction instances, protocols, structures and techniqueshave not been shown in detail in order not to obfuscate the description.

Terminology

Literature about metaheuristics or metaheuristic optimization uses alarge variety of loosely defined terms that vary based on the particularmetaheuristic algorithm being discussed. For instance, genetic algorithmand differential evolution algorithm literature refer to iterations asgenerations, a potential solution as an individual, and the quality of asolution within the context of a particular optimization problem asfitness. Particle swarm optimization algorithm literature refers to apotential solution as a bird or particle. Bee optimization algorithmliterature refers to a solution as a food source and the quality orfitness of a solution for the particular optimization problem as anectar amount. Despite the myriad of terms, population-basedmetaheuristic optimization algorithms evaluate potential solutions, andgenerate values that represent the quality of corresponding solutionswith respect to a particular optimization problem. This descriptionrefers to the solutions that are evaluated as “candidate solutions.”This description refers to a value that represents quality of acandidate solution for a particular optimization problem as a figure ofmerit. The term figure of merit is used within engineering for aquantity that characterizes performance of a design or measures a“degree of goodness” of a design with respect to alternatives. Thisdescription refers to the objective function (or group of functions)employed by a population-based metaheuristic algorithm to generate afigure of merit as a fitness function. This description refers tomultiple candidate solutions under consideration together (e.g., in asame iteration) as a population.

Although a candidate solution can be understood to encompass programcode, this description uses the terms “candidate solution” to refer todata or both data and program code. But a candidate solution, as usedherein, does not refer solely to program code. A candidate solution canhave a variety of structures (e.g., array, of values, list of parametersto be passed into a function/procedure, data structure, etc.). Althoughsome examples of the structure of an individual are provided, theexamples are not intended to limit the structure to that described, butare merely provided to help describe the inventive subject matter.

A population-based metateuristic algorithm may operate on a single dememodel or a multi-deme model. A deme refers to a local population unit.In a multi-deme model, a population of individuals is separated intosub-populations. Candidate solutions do not mix between demes ofsub-populations unless migration is implemented. When separated intosub-populations, the term “generation” typically refers to all of thesub-populations in that generation. The context of this discussion is,generally, a population within a single deme model or a sub-populationwithin a multi-deme model. The term “population” will be used, and whenreferring to another sub-population within the multi-deme model, theterm “foreign population” will be used.

The data of candidate solutions include parameters. This descriptionrefers to design parameters and context parameters. Design parametersrefer to the parameters of a design (e.g., wire length, spacing betweenwires, transmission rate, etc.). To comply with common use of the termsformal parameter and actual parameter, this description refers to actualdesign parameters when referring to actual parameters defined for adesign (e.g., 10 millimeters, 1 Mb/s). The term context parameter isused herein to refer to an environment variable or manufacturingvariables that is typically beyond control of a designer (e.g., ambienttemperature, interference, data pattern, etc.).

Overview

The search space or problem space to search for an optimal solution inworst-case scenarios is large because two aspects are being searchedfor: 1) the worst cases, and 2) the best of those worst cases. This canalso be expressed as searching for the best of the worst figures ofmerit. To find the worst figures of merit, the searching is driventowards solutions with the worst figures of merit based on an assumptionthat these worst figures of merit are occurring due to contextparameters that correspond to worst-case scenarios (e.g., highinterference). Although the search is driven toward solutions with lowerfigures of merit, a metaheuristic optimization algorithm advances withthe best of these lower figures of merit.

One approach for driving the search for the best of the worst is to do atwo-level nested optimization. The first level utilizes a metaheuristicoptimizer (i.e., an executing instance of program code that implements ametaheuristic optimization algorithm) to determine the actual designparameters that result in optimal figures of merit. The fitness functionof the first level then performs a second-level of optimization in whichthe actual design parameters are fixed based on the initial figures ofmerit from the first level. Another metaheuristic optimizer is used todetermine the worst-case for the candidate solutions by searching theoptimization problem space as defined by the context parameters for thefixed actual design parameters. The worst-case figures of meritgenerated by the second level of optimization are passed back for use bythe first level of optimization.

A more efficient technique uses a structure (e.g., data structure totrack figures of merit over iterations by actual design parameters forcandidate solutions that include both actual design parameters andactual context parameters. Instead of returning a current iterationfigure of merit, a worst observed figure of merit for a set of actualdesign parameters, which could be the current iteration figure of meritor a previously observed figure of merit, is returned as the figure ofmerit for a candidate solution. Since the candidate solution includesboth actual design parameters and actual context parameters and theworst observed figures of merit are tracked by actual design parameters,the figure of merit for a set of design parameters will be the worst ofthe observed worst case scenarios as defined by the actual contextparameters over a run of a metaheuristic optimizer. In other words, thesearch by the metaheuristic optimizer is guided by persisting worstobserved figures of merit by actual design parameters.

Description of Example Illustrations

FIG. 1 depicts an example conceptual diagram of a population-basedmetaheuristic optimizer persisting worst Observed figures of merit byactual design parameters. In this example depiction, thepopulation-based metaheuristic optimizer includes an evaluator 113, aworst case evaluator 117, and a metaheuristic advancer 121. Theevaluator 113 evaluates candidate solutions by simulating the candidatesolutions. For example, the evaluator may simulate operation of anintegrated circuit (IC) as defined by the actual parameters of acandidate solution and tinder conditions as defined by the actualcontext parameters of the candidate solution. Possible simulation by anevaluator can range from a network to a chip component. The worst caseevaluator 117 maintains data to persist worst observed figures of meritby actual design parameters. The metaheuristic advancer 121 performsoperations to advance the search to a next iteration. For example, themetaheuristic advancer 121 may perform reproduction and mutationoperations if the metaheuristic optimizer is based on a geneticalgorithm. The metaheuristic advancer 121 may adjust pheromone levels isthe metaheuristic optimizer is based on an ant colony optimizationalgorithm. The depicted example operations in FIG. 1 are identified by asequence of letters A-F that represent stages. Every possible operationof a metaheuristic optimizer is not depicted to avoid obfuscating thedescription. A line 100 separates depicted operations of differentiterations. The operations above the line 100 are for an early iterationwhite the operations below the line 100 are a later iteration.

At stage A, candidate solutions are input into the evaluator 113. Thecandidate solutions include candidate solutions it 101A-101N. Each ofthe candidate solutions includes actual design parameters and actualcontext parameters. The candidate solution 101A. includes actual designparameters 109A and actual context parameters 105A. The candidatesolution 101N includes actual design parameters 109N and actual contextparameters 105N. The candidate solutions 101A-101N may have beenrandomly generated or may be seed solutions (e.g., defined by adesigner).

At stage B, the evaluator 117 evaluates each of the candidate solutions101A-101N, If the actual design parameters define microprocessor, thenthe evaluator 117 simulates a microprocessor as defined by the actualdesign parameters in accordance with the actual context parameters. Forinstance, the actual context parameters 105A can include an actualambient temperature parameter of 130 degrees Fahrenheit. And theevaluator 113 may generate one or more performance values that representthe behavior of the microprocessor design in a 130 degree Fahrenheitenvironment (e.g., maximum frequency before failure). The actual designparameters 109N can be the same as the actual design parameters 109Awhile the actual context parameters 105N include an actual contextparameter of 95 degrees Fahrenheit.

At stage C, the evaluator 113 uses a fitness function 110 to generatefigures of merit for each of the candidate solutions based on results ofthe evaluation. The fitness function 110 is defined to generate a figureof merit for a candidate solution based on 1:n values yielded from theevaluation by the evaluator. As one example, the fitness function 110may generate a figure of merit based on a maximum processor frequencybefore failure. A more complex fitness function may generate a figure ofmerit with input of multiple evaluation results. For example, thefitness function 110 may generate a figure of merit based on input ofmaximum frequency before failure, time of operation, and instructionthroughput.

At stage D, the worst case evaluator 117 tracks the worst observedfigures of merit by design parameters. The worst case evaluator 117 usesa structure 115 to track the worst observed figures of merit by designparameters output by the fitness function 110. The structure 115includes a plurality of entries, each of which at least identifies a setof actual design parameters associated with worst observed figure ofmerit for that set of actual design parameters. The worst case evaluator117 uses a representation of each set of observed actual designparameters as an index into the structure 115. A variety of techniquescan be employed to uniquely represent each different combination ofactual design parameters that pass through the evaluator 117. Forexample, a hash function can be used to generate hashes for eachdifferent set of actual design parameters, As another example, the worstcase evaluator 117 can also create a string for each different set ofactual design parameters. The worst case evaluator 117 creates entriesfor each newly observed set of actual design parameters. When a set ofactual design parameters are observed in later iterations, thecorresponding worst observed figure of merit will be updated if worsethan what is currently stored in the structure 115. In this exampleillustration, the fitness function 110 outputs a figure of merit of 0.92for the candidate solution 101A and a figure of merit 0.99 for thecandidate solution 101N. The worst case evaluator 117 creates an entryfor the first candidate solution 109A with an index 0x12 that isgenerated from the actual design parameters 109A. The worst caseevaluator 117 also creates an entry for the candidate solution 101N withan index 0x3C that is generated from the actual design parameters 101N.In this early iteration, the worst case evaluator 117 has not yet seenthe set of actual design parameters 101A or 101N. Therefore, the figuresof merit for these candidate solutions are written by the worst caseevaluator 117 into the structure 115.

The figures of merit written into the structure 115 flow into astructure 119 that indicates figures of merit for a current populationof candidate solutions. The metaheuristic advancer 121 uses the figuresof merit in the structure 119 to perform the operations of theparticular population-based metaheuristic optimization algorithm toadvance the population of candidate solutions.

The operations of the tater iteration depicted below the line 100 focuson the actions of the evaluator 113 and the worst case evaluator 117, Asin earlier iterations, multiple candidate solutions are input into theevaluator 113 for evaluation. In this later iteration, a first candidatesolution includes the actual design parameters 109A and a set of actualcontext parameters 106A. A candidate solution N-1 includes the actualdesign parameters 109N and a set of actual context parameters 106N. Therecurrence of the actual design parameters in the same order acrossiterations is merely for ease of illustration. Embodiments are notconstrained to a strict ordering of candidate solutions by actual designparameters as may be (erroneously) inferred from the illustration. Theevaluator 113 generates one or more simulation results fir each inputcandidate solution. At stage E, the evaluator 113 uses the fitnessfunction 110 to generate a figure of merit for each of the candidatesolutions based on the simulation results. In this later iteration, FIG.1 depicts the fitness function 110 outputting a figure of merit 0.95 forthe first candidate solution and a figure of merit 0.87 for the N-1candidate solution.

At stage F, the worst case evaluator 117 updates entries in thestructure 115 for previously observed actual design parameter if thefigures of merit are worse. Although the first candidate solution, whichincludes the actual design parameters 109A and the actual contextparameters 106A, is different than the candidate solution 101A, theworst case evaluator 117 has already observed the set of actual designparameters 109A. Likewise, the worst case evaluator has already observedthe set of actual design parameters 109N even though the N-1 candidatesolution is different than the candidate solution 101N. Since the actualdesign parameters 109A have already been observed, the structure 115already has an entry indexed by 0x12. Likewise, the structure 115already has an entry indexed by 0x3C for the actual design parameters109N. Since 0.95 is better than the previously observed 0.92 for theactual design parameters 109N, the worst case evaluator will not persistthe figure of merit 0.95, Instead, the figure of merit 0.92 will bepassed to the structure 119 instead of the figure of merit 0.95. For theactual design parameters 109N, the figure of merit 0.87 for thecandidate solution is worse than the previously observed figure of merit0.99 for the candidate solution 101N. The worst case evaluator 117updates the entry for the actual design parameters 109N with the newworst observed figure of merit 0.87. This figure of merit 0.87 passes tothe structure 119. Thus, the metaheuristic advancer 121 will use 0.92for the first candidate solution and 0.87 for the N-1 candidatesolution.

Each of the evaluator 113, the worst case evaluator 117, and themetaheuristic advancer 121 are example modules that implement adifferent aspect of the metaheuristic optimizer. These are depicted asmodules to simplify depiction of the executing instance of program codeperforming one or more functions, Although depicted as disparatemodules, the functionality represented by the modules can be implementedas a single monolithic block of program code, library files, applicationprogramming interface functions, etc. For instance, the evaluator 113 isdepicted as including the fitness function 110. Implementation, however,can vary. The fitness function 110 can be a separately defined block ofprogram code method, procedure, function, etc.). The evaluator 113 maypass the results of simulation as parameters via library or API call.The evaluator 113 may pass the results of simulation to another modulethat manages the different aspects of a metaheuristic optimizer.

FIG. 2 depicts a flowchart of example operations for persisting theworst observed figure of merit across progression of a population-basedmetaheuristic optimizer. The example operations of FIG. 2 are those thatwould be performed by the program instructions that receive output froma fitness function and output to program instructions that progress apopulation of candidate solutions, For instance, the example operationswould be performed by program instructions represented by the worst caseevaluator in FIG. 1.

At block 201, a figure of merit is received for a candidate solution.For example, a block of program instructions is invoked by name with thefigure of merit and the candidate solution passed as parameters, eitherliterally or referentially, As another example, a process that persiststhe worst observed figures of merit by actual design parameters (“worstcase evaluator process”) may be running separately from a process thatimplements the fitness function. In that case, the process thatimplements the fitness function transmits one or more data packets thatconvey the candidate solution and the corresponding figure of merit tothe worst case evaluator process.

At block 203, it is determined whether the structure with the worstobserved figures of merit by actual design parameters (hereinafter“worst case structure”) has an entry for the actual design parameters ofthe candidate solution. For example, the worst case evaluator processgenerates a representative value (e.g., identifier or index) for the setof actual design parameters of the candidate solution. The worst caseevaluator process may construct a string with the set of actual designparameters, may generate a hash value, etc. The worst case evaluatorprocess then accesses the worst case structure with thisidentifier/index. The worst case evaluator process may compare theidentifier against each entry to look for a match in a variable sizeworst case structure (e.g., tree, linked list, etc.), for example. Theworst case evaluator process may index into the worst case structurewith the generated representation in a fixed size worst case structure(e.g., array, hash table, etc.). As another example, the worst caseevaluator process may use each actual design parameter of the set ofactual design parameters as an index into a. multi-dimensional worstcase structure. If the worst case structure contains an entry for theactual design parameters, then control flows to block 204. If the worstcase structure does not contain an entry for the actual designparameters, then control flows to block 205.

At block 205, a new entry is created in the worst case structure for theset of actual design parameters with the figure of merit. Creating thenew entry may involve allocation of additional memory in a variablesized worst case structure, or population of values into a fixed sizedworst case structure.

At block 207, the received figure of merit is supplied as the figure ofmerit for the candidate solution to the process that advances thepopulation of candidate solution. For example, the worst case evaluatorprocess may pass the figure of merit and an indication of the candidatesolution (or the candidate solution itself) to the metaheuristicadvancer via inter-process communication, network packets, etc. In otherimplementation, the worst case evaluator process writes the figure ofmerit into a structure for candidate solutions of a current iteration.

If the worst case structure has an entry for the set of actual designparameters as determined at block 203, then control flowed to block 204.At block 204, it is determined whether the figure of merit in the entryis worse than the received figure of merit. If the figure of meritcurrent associated in the worst case structure with the set of actualdesign parameters is worse than the received figure of merit, thencontrol flows to block 211. Otherwise, control flows to block 209.

At block 211, the received figure of merit is discarded. The figure ofmerit can be added to a heap for removal, immediately deleted, markedfor deletion, etc.

At block 213, the figure of merit in the entry is supplied as the figureof merit for the candidate solution. The received figure of merit can besupplied with various techniques as described with respect to block 207.

If the received figure of merit was determined to be worse than thefigure of merit in the entry at block 204, then control flowed to block209. At block 209, the entry is updated with the received figure ofmerit. The worst case evaluator process overwrites the figure of meritin the entry with the received figure merit, thus updating the worstcase structure to indicate the worst observed figure of merit for theset of actual design parameters. Embodiments do not necessarilyoverwrite the previous worst observed. figure of merit. Embodiments maymaintain a history of some or all of the figures of merit observed for aset of actual design parameters. Control flows from block 209 to block207.

A threshold can also be employed to avoid evaluation of some candidatesolutions. The worst case structure can be used with a threshold toshort circuit evaluation of candidate solutions. FIG. 3 depicts aflowchart of example operations that avoid evaluation of candidatesolutions with actual design parameters with previously observed worstfigures of merit already below a threshold (hereinafter “conservationthreshold”). The example operations are performed on candidate solutionsprior to the candidate solutions being submitted for simulation. Thisshort circuit technique conserves resources used for simulation and thefitness function.

At block 301, a candidate solution is received. The candidate solutionmay be passed into a function that implements candidate solutionsimulations. The candidate solution may be passed into a pre-processingfunction that determines whether evaluation can be skipped and avoidpassing the candidate solution into an evaluator.

At block 303, it is determined whether the worst case structure has anentry for the actual design parameters of the received candidatesolution. If an entry does not already exist, then control flows toblock 305. If an entry already exists, then control flows to block 307.

At block 307, it is determined whether the figure of merit in the entrysatisfied a conservation threshold. If a figure of merit is already tootow for further consideration by the metaheuristic optimizer, thenresources can be conserved by not further searching for an even worsefigure of merit. The conservation can be defined as an absolutethreshold. For example, the absolute conservation threshold may bedefined as 0.4 when figures of merit can range from 0 to 1. Embodimentscan also define a dynamic conservation threshold that is based on afitter candidate solution. For instance, the dynamic conservationthreshold can be defined as 10% of a greatest figure of merit observedso far in a current iteration. If a candidate solution has actual designparameters with a worst observed figure of merit that is 10% or less ofa figure of merit for a current frontrunner in the current iteration. Ifthe figure of merit in the entry satisfies the conservation threshold,then control flows to block 213 of FIG. 2. Otherwise, control flows toblock 305.

At block 305, the candidate solution is submitted for simulation. Thecandidate solution is passed to a metaheuristic evaluator for simulationand generation of a figure of merit.

Within an iteration, multiple candidate solutions may have a same set ofactual design parameters. This can lead to different figures of meritbeing supplied to the advancing stage for the different candidatesolution with the same set of actual design parameters. To enforceconsistency within an iteration, the previously observed figure of meritfor a set of actual design parameters can be supplied for populationadvancement. After figures of merit have been generated for thecandidate solutions in a current iteration, the worst figure of meritacross candidate solutions within the current iteration having a sameset of actual design parameters can be stored in the worst casestructure if worse than the previously observe figure of merit. FIG. 4depicts a flowchart of example operations to enforce consistency ofworst Observed figure of merit across observed same sets of actualdesign parameters within an iteration. The example operations of FIG. 4are similar to those in FIG. 2. The example operations of FIG. 4 differwith respect to how the worst case structure is maintained as depictedin blocks 407, 405, and 409.

At block 401, a figure of merit is receive for a candidate solution. Forexample, a block of program instructions is invoked by name with thefigure of merit and the candidate solution passed as parameters, eitherliterally or referentially, As another example, worst case evaluatorprocess may be running separately from a process that implements thefitness function, in that case, the process that implements the fitnessfunction transmits one or more data packets that convey the candidatesolution and the corresponding figure of merit to the worst caseevaluator process,

At block 403, it is determined whether the structure with the worstobserved figures of merit by actual design parameters (hereinafter“worst case structure”) has an entry for the actual design parameters ofthe candidate solution. For example, the worst case evaluator processgenerates a representative value (e.g., identifier or index) for the setof actual design parameters of the candidate solution. The worst caseevaluator process may construct a string with the set of actual designparameters, may generate a hash value, etc. The worst case evaluatorprocess then accesses the worst case structure with thisidentifier/index. The worst case evaluator process may compare theidentifier against each entry to look for a match in a variable sizeworst case structure (e.g., tree, linked list, etc.), for example. Theworst case evaluator process may index into the worst case structurewith the generated representation in a fixed size worst case structure(e.g., array, hash table, etc.). As another example, the worst caseevaluator process may use each actual design parameter of the set ofactual design parameters as an index into a multi-dimensional worst casestructure. If the worst case structure contains an entry for the actualdesign parameters, then control flows to block 407. If the worst casestructure does not contain an entry for the actual design parameters,then control flows to block 405.

At block 405, a new entry is created in the worst case structure for theset of actual design parameters with the figure of merit. The figure ofmerit is set as both the current worst observed figure of merit and theprevious worst observed figure of merit. The current worst observedfigure of merit is the worst figure of merit observed in the currentiteration for the set of actual design parameters. The previous worstobserved figure of merit is the worst figure of merit observed for theset of actual design parameters prior to the current iteration. Sincethe set of actual design parameter have not yet been observed, then thereceived figure of merit is used as both values. Creating the new entrymay involve allocation of additional memory in a variable sized worstcase structure, or population of values into a fixed sized worst casestructure. Control flows from block 405 to block 413.

If the worst case structure has an entry for the set of actual designparameters as determined at block 403, then control flowed to block 407.At block 407, it is determined whether the current worst observed figureof merit of entry is worse than the received figure of merit. If thecurrent worst observed figure of merit in the entry is worse than thereceived figure of merit, then control flows to block 411. If thereceived figure of merit is worse than the current worst observed figureof merit in the entry, then control flows to block 409.

At block 411, the received figure of merit is discarded. The figure ofmerit can be added to a heap for removal, immediately deleted, markedfor deletion, etc. Control flows from block 411 to block 413.

If the received figure of merit was determined to be worse than thecurrent worst observed figure of merit in the entry at block 407, thencontrol flowed to block 409, At block 409, the entry is updated with thereceived figure of merit as the current worst observed figure of merit.The worst case evaluator process overwrites the current worst figure ofmerit in the entry with the received figure merit, thus updating theworst case structure to indicate the worst observed figure of merit forthe set of actual design parameters within the current iteration.Control flows from block 409 to block 413.

At block 413, the previous observed worst figure of merit in the entryis supplied as the figure of merit for the candidate solution to theprocess that advances the population of candidate solution, For example,the worst case evaluator process may pass the previous worst observedfigure of merit and an indication of the candidate solution (or thecandidate solution itself) to the metaheuristic advancer viainter-process communication, network packets, etc. In otherimplementation, the worst case evaluator process writes the previousworst observed figure of merit into a structure for candidate solutionsof a current iteration used by the metaheuristic advancer. Effectively,the metaheuristic advancer will use the same worst figure of meritobserved up to the current iteration across candidate solutions in thecurrent iteration having the same set of actual design parameters.Possible delay of a figure of merit that is worse than a previousobserved figure of merit allows enforcement of consistency across thecandidate solutions with the same set of actual design parameters. Thisreduces the chances of propagating actual context parameters that do notdefine worst case scenarios. In other words, this consistency constraintreduces the chances of the metaheuristic optimizer being “distracted” bya candidate solution with actual context parameters that define aneasier environment and/or manufacturing variables than a candidatesolution with actual context parameters that define a worse situation.

To enforce consistency, figures of merit are observed across thecandidate solutions of a current iteration before updating the previousworst observed figure of merit. FIG. 5 depicts an example flowchart ofoperations for updating the previous observed worst figure of merit.

At block 501, an indication that a current iteration has completedevaluation is received, For example, the worst case evaluator processreceives a communication from the metaheuristic evaluator process thatthe last candidate solution of the current iteration has been evaluatedand a figure of merit generated therefor. As another example, the worstcase evaluator process periodically checks for a flag to be set by themetaheuristic evaluator that indicates completed evaluation for aniteration. In some cases, the worst case evaluator process can be awareof a fixed number of candidate solutions to be evaluated at eachiteration. The worst case evaluator process can track the number ofcandidate solutions within an iteration itself and determine when it hasreceived figures of merit for all candidate solutions of an iteration.

At block 503, a loop of operations begins for each entry in the worstcase structure. In this example illustration, the loop of operationsincludes blocks 505 and 507.

At block 505, it is determined whether the current worst figure of merit(i.e., the worst figure of merit observed in the current iteration) ofthe entry is worse than the previous worst figure or merit of the entry.if the current worst figure of merit is worse than the previous worstfigure of merit then control flows to block 507. Otherwise, controlflows to block 509.

At block 507, the previous worst formal parameter of the entry is set tothe current worst figure of merit of the entry. For instance, the worstcase evaluator process overwrites the previous worst figure of meritwith the current worst figure of merit. Control flows from block 507 toblock 509.

At block 509, it is determine whether all entries have been examined. Ifnot, then control flows back to block 503. If so, then control flows toblock 511 where it is indicated that the worst case structure has beenupdated. The indication can be used to allow the worst case evaluatorprocess to being evaluating figures of merit from a next iteration.

Variations from Depicted Example Illustrations

Embodiments may manipulate figures of merit to further steer ametaheuristic optimizer to search for new worst observed figures ofmerit. When a candidate solution has actual design parameters that causean update to the worst case structure, the worst case evaluator processcan manipulate the figure of merit for the candidate solution or thecandidate solution itself to increase the likelihood that the candidatesolution will be used to advance the population of candidate solutions.For example, a worst case evaluator process may augment a figure ofmerit that is supplied to a metaheuristic advancer but not augment thefigure of merit that is stored in the worst case structure. The worstcase evaluator process can mark the candidate solution to be used inadvancing the population of candidate solutions regardless of the figureof merit when the actual design parameters of the candidate solutioncause an update to the worst case structure. This avoids corrupting thefigures of merit. To prevent influence of unacceptable candidatesolutions, thresholds can be defined to override marked candidatesolutions. For example, the metaheuristic advancer will use a markedcandidate solution to advance to a next iteration unless the figure ofmerit supplied for the candidate solution falls below a minimumacceptable figure merit, which would be distinct from a threshold usedin selecting candidate solutions for advancing the population.

The example operations depicted in the flowcharts are intended to aid inunderstanding the inventive subject matter and should not be used tolimit embodiments of the inventive subject matter. Embodiments mayperform operations in a different order, in parallel, additionaloperations, or fewer operations. The example operations of FIG. 2presume an implementation that passes each figure of merit to the worstcase evaluator program instructions. Embodiments are not limited to aparticular technique for passing input, though. Embodiments can pass thefigures of merit in a batch to the program instructions that persist theworst observed figures of merit by actual design parameters. Also,embodiments may not discard a figure of merit as depicted with block 211of FIG. 2, Embodiments may record the figure of merit for togging,analysis, or other purposes.

Multi-Deme Architecture

FIG. 6 depicts an example network of nodes carrying out a multi-dememodel of a population-based metaheuristic optimization algorithm thatuses worst case evaluators. A network of nodes 600 is depicted withseveral nodes communicatively coupled via a network 614, which can beimplemented in accordance with any of a variety of network technologies.A node 601 hosts a global metaheuristic process manager 607. The globalmetaheuristic process manager 607 allocates and manages resources forthe metaheuristic process and monitors progress and results of localdenies. A node 603 hosts a fitness evaluator 605. The fitness evaluator605 runs simulations and compute figures of merit based on a definedfitness function.

FIG. 6 depicts three nodes responsible for local demes. A node 609 hostsa deme manager 615 and a worst case evaluator 617. A node 611 hosts ademe manager 619 and a worst case evaluator 621. A node 613 hosts a dememanager 623 and a worst case evaluator 625. The deme managers eachgenerate initial local demes or sub-populations, unless assigned to themby the global evolutionary process manager 607. Each of the dememanagers reports progress of their local deme to the global evolutionaryprocess manager periodically and/or in response to a request from theglobal evolutionary process manager 607. Each of the worst caseevaluators influences searching of the optimization problem space bypersisting worst observed figures of merit within their respective localdente. Each of the deme managers can invoke their corresponding worstcase evaluators in a manner similar to that depicted in any of FIGS.2-5. The network of nodes 600 depicted in FIG. 6 is an example and cantake different forms or configurations. For example, multiple nodes maycarry out fitness evaluation. The network can be configured to assign afitness evaluator for a given number of demes, or even per dente.

As will be appreciated by one skilled in the art, aspects of the presentinventive subject matter may be embodied as a system, method or computerprogram product. Accordingly, aspects of the present inventive subjectmatter may take the form of an entirely hardware embodiment, an entirelysoftware embodiment (including firmware, resident software, micro-code,etc.) or an embodiment combining software and hardware aspects that mayall generally be referred to herein as a “circuit,” “module” or“system.” Furthermore, aspects of the present inventive subject mattermay take the form of a computer program product embodied in one or morecomputer readable medium(s) having computer readable program codeembodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent inventive subject matter may be written in any combination ofone or more programming languages, including an object orientedprogramming language such as Java, Smalltalk, C++ or the like andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The program codemay execute entirely on the user's computer, partly on the user'scomputer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer may beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection may be made to an external computer (for example, through theInternet using an Internet Service Provider).

Aspects of the present inventive subject matter are described withreference to flowchart illustrations and/or block diagrams of methods,apparatus (systems) and computer program products according toembodiments of the inventive subject matter. It will be understood thateach block of the flowchart illustrations and/or block diagrams, andcombinations of blocks in the flowchart illustrations and/or blockdiagrams, can be implemented by computer program instructions. Thesecomputer program instructions may be provided to a processor of ageneral purpose computer, special purpose computer, or otherprogrammable data processing apparatus to produce a machine, such thatthe instructions, which execute via the processor of the computer orother programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

FIG. 7 depicts an example computer system with a metaheuristic solverthat employs worst case evaluation. A computer system includes aprocessor unit 701 (possibly including multiple processors, multiplecores, multiple nodes, and/or implementing multi-threading, etc.). Thecomputer system includes memory 707. The memory 707 may be system memory(e.g., one or more of cache, SRAM, DRAM, zero capacitor RAM, TwinTransistor RAM, eDRAM, EDO RAM, DDR RAM, EEPROM, NRAM, RRAM, SONOS,PRAM, etc.) or any one or more of the above already described possiblerealizations of machine-readable media. The computer system alsoincludes a bus 703 (e.g., PCI, ISA, PCI-Express, HyperTransport® bus,InfiniBand® bus, NuBus, etc.), a network interface 705 (e.g., an ATMinterface, an Ethernet interface, a Frame Relay interface, SONETinterface, wireless interface, etc.), and a storage device(s) 709 (e.g.,optical storage, magnetic storage, etc.). The computer system alsoincludes a metaheuristic solver 725. The metaheuristic solver 725 isdepicted in this example as including a worst case evaluator 726. Themetaheuristic solver 725 generates candidate solutions, evaluatescandidate solutions, generates figures of merit, and performs operationsto progress a metaheuristic instance. The worst case evaluator 726persists worst observed figures of merit by actual design parameters toinfluence the metaheuristic solver 725 to explore worst case scenarios.The worst case evaluator 726 can also use the information about worstobserved figures of merit to avoid simulations. Any one of thesefunctionalities may be partially (or entirely) implemented in hardwareand/or on the processing unit 701. For example, the functionality may beimplemented with an application specific integrated circuit, in logicimplemented in the processing unit 701, in a co-processor on aperipheral device or card, etc. Further, realizations may include feweror additional components not illustrated in FIG. 7 (e.g., video cards,audio cards, additional network interfaces, peripheral devices, etc.).The processor unit 701, the storage device(s) 709, and the networkinterface 705 are coupled to the bus 703. Although illustrated as beingcoupled to the bus 703, the memory 707 may be coupled to the processorunit 701.

While the embodiments are described with reference to variousimplementations and exploitations, it will be understood that theseembodiments are illustrative and that the scope of the inventive subjectmatter is not limited to them. In general, techniques for steering ametaheuristic optimizer or solver to explore the worst cases in anoptimization problem space as described herein may be implemented withfacilities consistent with any hardware system or hardware systems. Manyvariations, modifications, additions, and improvements are possible.

Plural instances may be provided tor components, operations orstructures described herein as a single instance. Finally, boundariesbetween various components, operations and data stores are somewhatarbitrary, and particular operations are illustrated in the context ofspecific illustrative configurations. Other allocations of functionalityare envisioned and may fall within the scope of the inventive subjectmatter. In general, structures and functionality presented as separatecomponents in the exemplary configurations may be implemented as acombined structure or component. Similarly, structures and functionalitypresented as a single component may be implemented as separatecomponents. These and other variations, modifications, additions, andimprovements may fall within the scope of the inventive subject matter.

1.-8. (canceled)
 9. A computer program product for guiding apopulation-based metaheuristic search for an optimization problem, thecomputer program product comprising: a computer readable storage mediumhaving computer usable program code embodied therewith, the computerusable program code comprising a computer usable program code to: foreach candidate solution in a current iteration of a population-basedmetaheuristic instance, determine whether a figure of merit generatedfrom a fitness function of the population-based metaheuristic instancefor the candidate solution is worse than a figure of merit associatedwith actual design parameters of the candidate solution in a structureused to track worst observed figures of merit by actual designparameters over iterations, wherein the actual design parameters are asubset of actual parameters of the candidate solution; update thestructure to associate the figure of merit with the actual designparameters when the figure of merit generated for the candidate solutionin the current iteration is worse than a previously observed worstfigure of merit for the actual design parameters in the structure; andsupply, as a figure of merit to be used for the candidate solution inadvancing the population-based metaheuristic instance, the worst betweenthe figure of merit generated for the candidate solution in the currentiteration and the previously observed worst figure of merit for theactual design parameters.
 10. The computer program product of claim 9further comprising computer usable program code to create an entry inthe structure when the structure does not have an entry for actualdesign parameters of a candidate solution.
 11. The computer programproduct of claim 10, wherein the computer usable program code to createthe entry comprises computer usable program code to generate an indexfor the entry based, at least in part, on the actual design parametersof the candidate solution for which there was no entry.
 12. The computerprogram product of claim 9, wherein the computer usable program code tosupply the worst between the figure of merit generated for the candidatesolution in the current iteration and the previously observed worstfigure of merit for the actual design parameters comprises computerusable program code to update a second structure, which indicatesfigures of merit for candidate solutions of the current iteration of thepopulation-based metaheuristic instance, to associate the candidatesolution with the worst between the figure of merit generated for thecandidate solution in the current iteration and the previously observedworst figure of merit for the actual design parameters.
 13. The computerprogram product of claim 9 further comprising computer usable programcode to: for each candidate solution in the current iteration of thepopulation-based metaheuristic instance, prior to evaluation of thecandidate solution and generation of a figure of merit with the fitnessfunction, determine whether the structure indicates a previouslyobserved worst figure of merit for actual design parameters of thecandidate solution that satisfied a threshold; obviate evaluation of thecandidate solution and supply the previously observed worst figure ofmerit associated with the actual design parameters of the candidatesolution in the structure when the previously observed worst figure ofmerit satisfies the threshold.
 14. The computer program product of claim9 further comprising computer usable program code to: augment the figureof merit to be supplied and used for a candidate solution in advancingthe population-based metaheuristic instance when the figure of merit isthe worst between the figure of merit generated for the candidatesolution in the current iteration and the previously observed worstfigure of merit for the actual design parameters of the candidatesolution.
 15. The computer program product of claim 9, wherein thecomputer usable program code to update the structure to associate thefigure of merit with the actual design parameters when the figure ofmerit generated for the candidate solution in the current iteration isworse than a previously observed worst figure of merit for the actualdesign parameters in the structure comprises computer usable programcode to update the structure to associate the figure of merit with theactual design parameters when the figure of merit generated for thecandidate solution in the current iteration is worse than a previouslyobserved worst figure of merit for the actual design parameters in thestructure and a worst of the figures of merit observed in the currentiteration for the actual design parameters.
 16. The computer programproduct of claim 15 further comprising computer usable program code to:after figures of merit have been generated for the candidate solutionsof the current iteration of the population-based metaheuristic instance,for each entry of the structure that indicates a worst figure of meritobserved in the current iteration for actual design parameterscorresponding to the entry that is worse than the previously observedworst figure of merit for the actual design parameters corresponding tothe entry, update the previously observed worst figure of merit to bethe worst figure of merit observed in the current iteration.
 17. Anapparatus for guiding a population-based metaheuristic search for anoptimization problem, the apparatus comprising: a processor; a networkinterface; and a computer readable storage medium having computer usableprogram code embodied therewith, the computer usable program codecomprising a computer usable program code to: for each candidatesolution in a current iteration of a population-based metaheuristicinstance, determine whether a figure of merit generated from a fitnessfunction of the population-based metaheuristic instance for thecandidate solution is worse than a figure of merit associated withactual design parameters of the candidate solution in a structure usedto track worst observed figures of merit by actual design parametersover iterations, wherein the actual design parameters are a subset ofactual parameters of the candidate solution; update the structure toassociate the figure of merit with the actual design parameters when thefigure of merit generated for the candidate solution in the currentiteration is worse than a previously observed worst figure of merit forthe actual design parameters in the structure; and supply, as a figureof merit to be used for the candidate solution in advancing thepopulation-based metaheuristic instance, the worst between the figure ofmerit generated for the candidate solution in the current iteration andthe previously observed worst figure of merit for the actual designparameters.
 18. The apparatus of claim 17 further comprising computerusable program code to: augment the figure of merit to be supplied andused for a candidate solution in advancing the population-basedmetaheuristic instance when the figure of merit is the worst between thefigure of merit generated for the candidate solution in the currentiteration and the previously observed worst figure of merit for theactual design parameters of the candidate solution.
 19. The apparatus ofclaim 17, wherein the computer usable program code to update thestructure to associate the figure of merit with the actual designparameters when the figure of merit generated for the candidate solutionin the current iteration is worse than a previously observed worstfigure of merit for the actual design parameters in the structurecomprises computer usable program code to update the structure toassociate the figure of merit with the actual design parameters when thefigure of merit generated for the candidate solution in the currentiteration is worse than a previously observed worst figure of merit forthe actual design parameters in the structure and a worst of the figuresof merit observed in the current iteration for the actual designparameters.
 20. The apparatus of claim 19 further comprising computerusable program code to: after figures of merit have been generated forthe candidate solutions of the current iteration of the population-basedmetaheuristic instance, for each entry of the structure that indicates aworst figure of merit observed in the current iteration for actualdesign parameters corresponding to the entry that is worse than thepreviously observed worst figure of merit for the actual designparameters corresponding to the entry, update the previously observedworst figure of merit to be the worst figure of merit observed in thecurrent iteration.